Question:medium

If \[ x=e^{\tan^{-1}\left(\frac{y-x^2}{x}\right)} \] then \(\dfrac{dy}{dx}=?\)

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For equations involving \(e^{\tan^{-1}(\cdot)}\), first take \(\log_e\) on both sides and then apply tangent to remove \(\tan^{-1}\).
Updated On: Jun 6, 2026
  • \(\sec^2(\log_e x)+\tan(\log_e x)\)
  • \(2x+\sec^2(\log_e x)+\tan(\log_e x)\)
  • \(-2x+\sec^2(\log_e x)+\tan(\log_e x)\)
  • \(2x+\sec(\log_e x)+\tan(\log_e x)\)
Show Solution

The Correct Option is B

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